# In Cixin Liu’s “Remembrance of Earth's Past" trilogy, why does it take the Trisolaran fleet 400 years to reach the solar system?

In Cixin Liu’s Remembrance of Earth's Past trilogy, why does it take the Trisolaran fleet 400 years to reach the solar system if it can achieve a speed of 1/10 the speed of light, given that Alpha Centauri is only 4.4 light years away? Even accounting for a 1g acceleration then deceleration, wouldn’t it take only 50 years or so?

• Simple arithmetic would suggest that a vessel traveling at 0.1 the speed of light would take at least 40 years to cover a distance of 4 light years or more, and that's assuming it traveled at its top speed constantly from start to finish. If the journey actually took 400 years rather than 40, it would suggest the vessel was only moving at around 0.01 the speed of light rather than 0.1. Not sure any of this is on-topic for this site though. Apr 6, 2021 at 14:14
• In the novel it is stated that the Trisolaran feet can travel at 1/10 the speed of light, hence my confusion. Apr 6, 2021 at 14:16
• I haven't read those books, but perhaps the 400 years figure is some sort of typo or miscalculation on the author's part then, and the correct journey time was approximately 40 years, rounding down to one significant figure. It does seem noteworthy that the actual figure given (400 years) is precisely 10 times what it should be (if the given speed is correct), and that the numerical inconsistency can be rectified by simply removing a zero from 400. Apr 6, 2021 at 14:34
• @LogicDictates It is not an error; it is a major part of the plot. (The actual figure is something like 450 years, IIRC.) Apr 6, 2021 at 14:38
• @DavidW Since they plan to colonize earth I assumed they can withstand 1g, but you're right, there's no evidence of it. Perhaps they can only achieve a much smaller acceleration, about 0.0001g assuming they reach their stated top speed of 1/10 speed of light at mid course, if my calculations are correct. Apr 6, 2021 at 15:12

This apparent paradox is addressed explicitly by Liu when Ye Wenjie is being interrogated. Just as the OP asks:

INTERROGATOR: Then I have a question. If the Trisolaran Fleet that had been launched is capable of flight at one-tenth the speed of light, it should take only forty years to reach the solar system. So why do you say that it would take more than four hundred years?

YE: Here’s the thing. The Trisolaran Interstellar Fleet is composed of incredibly massive spaceships. Accelerating them is a slow process. One-tenth the speed of light is only their maximum speed, but they cannot cruise at this speed for long before decelerating as they approach the Earth. Also, the source of propulsion for the Trisolaran ships is matter-antimatter annihilation. In front of each ship is a large magnetic field shaped like a funnel to collect antimatter particles from space. This collection process is slow, and only after a long wait can it gather enough antimatter to allow the ship to accelerate for a brief period. Thus, the fleet’s acceleration occurs in spurts, interspersed by long periods of coasting to collect fuel. This is why the time it takes the Trisolaran Fleet to reach the solar system is ten times longer than the flight time of a small probe.

• Thank you very much! Apr 6, 2021 at 15:29
• @DavidW interstellar space is not empty: en.wikipedia.org/wiki/Interstellar_medium Apr 6, 2021 at 15:46
• @LogicDictates trying to but the system won't let me as I originally posted the OP anonymously, my mistake :( Apr 6, 2021 at 15:48
• @Antoine Conze - Please try to merge the two accounts by following the instructions given here. If it works, you'll then be able to accept the answer. Apr 6, 2021 at 15:52
• @JanSpurny Did I say it was empty? I said it didn't contain antimatter. If the book had used a Bussard Ramjet, at least that would have been plausible. Apr 6, 2021 at 16:13

This could be a mistake if he assumed a constant acceleration to the mid point and and then constant deceleration to the target (Earth).

The acceleration that would allow a max speed of.15C, where C is the speed of light (3x10^8 m/s) at the center point of the journey, is .005G, where G is 1 Earth gravity (9.8m/s/s). At that acceleration, a trip of 4.4 light years would take 58 years, both Earth time and ship time.

In order for that 4.4 light year journey to take ~450 years, the acceleration would need to be .000086G and the max speed would be .019C.

All this is assuming a constant acceleration. Given this assumption, Cixin Liu's science displays a bit of hand waving and seems to be a plot device. He needed Earth to experience several generations of time to prepare. There are other problems with his story as well, in my opinion, but I'll keep that to myself.

See the relativistic travel calculator below.

http://convertalot.com/relativistic_star_ship_calculator.html

• Hi, welcome to SF&F. Note that the other answer contains quotes that explain the acceleration was in short bursts at long intervals. (Which ultimately is largely the equivalent of a very low average acceleration.) Aug 16, 2022 at 21:18